"The yard has a garden."
Translation:Η αυλή έχει κήπο.
This would be "Η αυλή έχει έναν κήπο" because ένας must be in the same case as the noun κήπος, in this sentence the accusative. It would be right this way. It's better to say "Η αυλή έχει κήπο" though, because the use of ένας in this sentence gives a meaning of "one and only".
αυλή is used for an open, "fenced" space that belongs to a house or a building (can sometimes be used interchangeably with προαύλιο), and
κήπος is an open, usually "fenced" (and sometimes, bigger than αυλή) area with plants , trees and flowers, again -most of the times- as part of a house or a building.
I hope this helps a bit ^.^
What it means is that there is a "yard" a piece of ground near the house/ around the house. And there is a "garden", an area with plants, flowers, etc, in that yard.
There is no indication that the "κήπος/garden" is bigger. Naturally, the "αυλή/yard" is bigger since it contains the "κήπος/garden".
"The garden has a garden" doesn't make much sense, neither in US nor in UK English :P Also, ιδιοκτησία is the direct transaltion of property, so that would probably cause some confusion.
However, since most UK speakers know the meaning of the sentence in US English as well, and the course's English is US English (officially), it might be better to just stick to the main translation, as it is. We always try to include as many UK alternatives as we possibly can, to please most learners, but sometimes, (like in this case), it's pretty hard to do so. :P